The present invention relates to techniques for correcting errors, and more particularly, to techniques for correcting errors using iterative decoding in data storage devices, such as hard disk drives.
Error correcting codes are used in data recording devices to ensure data reliability and to reduce the adverse effects of channel noise. Parity codes are examples of error correction codes. Parity codes are often used to correct errors that occur in data transmitted over a communications channel or stored on a digital storage medium. For example, parity check codes are often used to correct errors in data stored on magnetic hard disks.
Error correction decoding can be performed using hard decision decoders or soft-decision decoders. Hard decision decoding is generally based on an assumption that all bits in a codeword are equally likely to be in error. Hard decision decoding generally does not consider that some bits are more reliable than others. However, some hard decision decoding codes do provide un-equal protection to recorded bits.
Soft-decision decoding receives input analog data (e.g., an equalized read-back signal or bit reliability information) and preferentially flips unreliable bits. In soft decision decoding, the log-likelihood ratio (LLR) is a measure of the likelihood of a bit being a ‘1’ divided by the likelihood of the bit being ‘0.’ A greater absolute value of LLR indicates a more reliable bit. A soft decision decoder uses the LLR for each bit to evaluate the probability that the bit is in error. Soft-decision decoding out-performs hard-decision decoding, because it is able to exploit the fact that some bits are more reliable than others.
A low density parity check (LDPC) code is a linear error-correcting code that has a parity check matrix H with a small number of nonzero elements in each row and column. LDPC codewords can be decoded using soft-decision decoding. LDPC codes can be defined over any finite field. For example, an LDPC codes can be defined over a Galois field GF(2), in which “1” is the only nonzero element. The row (or column) weight (or degree) of an LDPC code refers to the number of elements that have a non-zero value among the numbers in rows (or columns) of the parity check matrix.
In a standard encoding process, a block of information bits is encoded using a generator matrix that can be derived from the parity check matrix of a LDPC code. In soft-decision decoding, the strength of error protection that is provided to each bit depends on the weight of the corresponding column in the parity check matrix that is used to decode the codewords. Bits corresponding to the columns with a lower weight are provided less error protection.
Some types of error detection schemes are iterative. One problem with iterative error detection schemes is that they tend to cause error propagation and to have an unacceptable error floor when used in magnetic hard disk drives. Also, many iterative error detection schemes used in magnetic hard disk drives have a high degree of complexity.
Therefore, it would be desirable to provide iterative techniques for correcting errors that cause less error propagation and that do not have a high degree of complexity. It would also be desirable to provide iterative techniques for correcting errors that have a controllable error floor.